If you're an International Man/Woman of Mystery, you can choose one of the other options with the understanding that while they more thoroughly overwrite your data, they take a very long time to do so. It's adequate for most people (though you'll want to keep an eye on this story's comments as some people have nearly religious views on this matter). The default, Zero Out Deleted Files, writes zeros over the drive's free space. Under Lion you see a slider that offers essentially the same options. With Snow Leopard this sheet offers Zero Out Deleted Files, 7-Pass Erase of Deleted Files, and 35-Pass Erase of Deleted Files. A sheet will appear that offers you different levels of erasure.

To do this, launch Disk Utility (/Applications/Utilities), select the drive that you want to work with, click the Erase tab, and click on Erase Free Space. This seeks out any areas of the drive marked as available for new data and overwrites them with junk. While you can't go back and target specific deleted files for 'no really, I want you totally gone' erasure, you can erase the 'free' space on your Mac's hard drive. The option to turn on 'Empty Trash securely' in the Finder advanced.

When you do this not only is the file removed from the Mac's directory, but the hard drive space it occupied is overwritten with junk. Today I saw the the menu item 'Secure Empty Trash' in the Finder menu was disabled. To delete a file so that it's unrecoverable by all but those who make their living recovering data, toss the file into the Trash and instead choose Finder -> Secure Empty Trash. What it does is tell the system to mark the space on the drive occupied by the files in the Trash as available to be overwritten.

Enable secure empty trash mac